The invention relates in general to operations performed at sea for acquiring geophysical data by means of a ship towing one or more cables associated with hydrophones.
More precisely, the invention relates to a method enabling the deformation of the cables towed by a ship to be predicted effectively, and it enables advantage to be taken of such prediction.
The purpose of geophysics is to describe the structure of the subsoil. The technique in widest use is reflection seismic surveying. When surveying off-shore, the principle is to emit a high power sound pulse towards the subsoil; the sound wave created in this way is reflected partially at the interfaces between the successive geological layers it encounters, and it returns towards the surface where hydrophones transform the sound signal into electrical signals.
In off-shore surveying, the sound source is generally constituted by air guns, and the hydrophones are grouped together in groups which are integrated in cables known as xe2x80x9cstreamersxe2x80x9d that are towed by the ship.
The number of sound sources and streamers, and the lengths of the streamers can be varied. Depending on required resolution, the distance between two consecutive groups varies over the range 12.5 meters (m) to 25 m. A simple configuration having two streamers S1 and S2, a single sound source Sa, and a plurality of groups T is shown in FIG. 1.
This figure also shows the so-called xe2x80x9ccommon midpointsxe2x80x9d (CMPs) that, for each {source, group} pair correspond to the subsurface point of reflection.
In practice, interaction between sea currents and immersed streamers gives rise to geometrical deformations in the system constituted by said streamers and the set of towed elements, thereby compromising the uniformity of coverage in the zone whose subsoil is to be characterized. These deformations vary in time and give rise to coverage xe2x80x9cholesxe2x80x9d which need to be filled in by additional passes of the boat, a process known as xe2x80x9cinfillingxe2x80x9d.
This constitutes a major drawback since additional passes increase the time required to perform operations and can give rise to very significant increases in cost (which can be as much as 20%).
In addition, the extra time and cost associated with infilling can vary very greatly from one operation to another, and it is therefore not possible to predict them accurately, thus preventing operators from giving accurate predictions concerning the time and cost of a projected operation; this constitutes an additional drawback for operators.
It will thus be understood that there exists a manifest need to reduce infilling and also to predict the amount of infilling that will be required in a projected data acquisition operation. In order to satisfy these needs, it is necessary to characterize the influence of current on streamer deformation.
In this respect, attempts have been made to model the deformation of a streamer towed by a ship and subjected to current. For example, reference can be made to the article xe2x80x9cThe shape of a marine streamer in a cross-currentxe2x80x9d by P. P. Krail and H. Brysk, published in Vol. 54, No. 3 of the journal of the Society of Exploitation Geophysicists.
However, such attempts do not reproduce real current conditions (the article mentioned assumes in particular that the current is steady and the ship follows a uniform rectilinear path) and a result the results thereof are unsuitable for being used directly so the above drawbacks remain.
The object of the invention is to enable those drawbacks to be reduced.
To achieve this object, the invention firstly provides a method of simulating the positioning of a streamer towed by a ship during an operation of acquiring geophysical data at sea, said acquisition operation making use of shots from at least one sound source, the method implementing a hydrodynamic model of the interaction between marine current, the path of the ship, and the streamer, the method being characterized in that it includes determining variations in the current over time and in space.
Other preferred, but non-limiting features of the method of the invention for simulating the positioning of a streamer are as follows:
the method comprises:
receiving primary current values as measured and/or predicted;
defining vector fields or xe2x80x98current objectsxe2x80x99 of respective types corresponding to different representations of the current and built up from said primary current values; and
selecting a xe2x80x98current objectxe2x80x99 as a function of the intended application;
xe2x80x98current objectxe2x80x99 selection takes account of proximity in time between the instant for which the prediction is made and the instant at which prediction is performed;
xe2x80x98current objectxe2x80x99 selection takes account of correlation between earlier xe2x80x98current objectxe2x80x99 predictions and measurements of current performed at the instants for which said earlier predictions were made;
the coordinates of at least some xe2x80x98current objectsxe2x80x99 comprise values measured on site;
the coordinates of at least some xe2x80x98current objectsxe2x80x99 comprise extrapolated values predicting current;
some xe2x80x98current objectsxe2x80x99 are computed by using a predictor filter enabling a current data series to be extrapolated from measurements of current made in the acquisition zone;
the defined types of xe2x80x98current objectxe2x80x99 comprise the following types:
1) total current as measured by a current meter;
2) tidal current as derived from meteorological bulletins, or as deduced from measurements of current by harmonic analysis;
3) the sum of a tidal current plus a residual current, said tidal current being derived from meteorological bulletins or being deduced from measurements of current by harmonic analysis, and said residual current being taken from meteorological bulletins;
4) an extrapolation from total current as measured by a current meter;
5) the sum of a tidal current and a computed residual current, said tidal current being taken from meteorological bulletins or being deduced from measurements of current by harmonic analysis, and said residual current being obtained by subtracting said tidal current from the current measured in the acquisition zone;
6) a history of past extrapolations of the total current as measured by a current meter; and
7) the sum of a tidal current and a history of past extrapolations of a series of values constituted by the total current as measured by a current meter from which a tidal current has been subtracted, said tidal current being taken from meteorological bulletins or being deduced from measurements of current by harmonic analysis;
while computing xe2x80x98current objectsxe2x80x99 of types 4, 5, 6, or 7, the processed data series is considered as a second order non-centered steady random process;
while computing values of a xe2x80x98current objectxe2x80x99 of type 4, 5, 6, or 7, weights are given to the measurements of the data series for extrapolation, which weights are inversely proportional to their age, for the purpose of anticipating sudden changes due to the residual current;
while computing a particular value of a xe2x80x98current objectxe2x80x99 of type 4, 5, 6, or 7, a variance function of the difference between the predicted value and the exact value of the current or the residual current at the instant for which the prediction was computed is minimized, where said variance function has the form:   G  =            (              1        -        1        -                              ∑                          i              =              3                                      P              +              1                                ⁢                                    a              i                        ⁢                          a              3                        ⁢                          xe2x80x83                        ⁢            ⋯            ⁢                          xe2x80x83                        ⁢                          a                              p                +                1                                                        )        ⁢                  Γ        U            ⁡              (                                            1                                                                                            -                  1                                -                                                      ∑                                          i                      =                      3                                                              P                      +                      1                                                        ⁢                                      a                    i                                                                                                                          a                3                                                                        ⋮                                                                          a                                  P                  +                  1                                                                    )            
while computing a particular value of a xe2x80x98current objectxe2x80x99 of type 4, 5, 6, or 7, an autocorrelation function of the current or residual current data series is computed, and then a linear system of equations is set up and solved;
while computing a particular value of a xe2x80x98current objectxe2x80x99 of type 4, 5, 6, or 7, the linear system to be solved is conditioned by implementing a descent method, preferably the conjugate gradient method;
the method provides the option of computing extrapolated values on a series of measured current values from which a tidal current has previously been subtracted so as to compute an extrapolated residual current, and then adding the tidal current corresponding to the instant for which the extrapolation has been made to said extrapolated residual current;
the method comprises estimating the performance of different predictions of current by comparison with a measurement of current performed at the time corresponding to the time of the predictions;
the method comprising estimating the performance of a xe2x80x98current objectxe2x80x99 derived from predictions and/or measurements of current by comparing the measured streamer positioning and the simulated streamer positioning, said simulation taking account of the xe2x80x98current objectxe2x80x99 whose performance is to be estimated; and
the performance of the xe2x80x98current objectxe2x80x99 is described by criteria which comprise the average of the absolute value of the difference between measurement and simulation of streamer positioning, and/or the difference between predicted and measured streamer positioning below the value for which 90% of the prediction points are to be found.
The invention also provides a method of assisting the navigation of a ship towing at least one streamer in order to reduce zones of undercoverage and/or overcoverage generated during a geophysical data acquisition operation at sea during which the ship travels along a plurality of lines extending in a general direction defining an abscissa and forming an array covering a desired zone, the method being characterized in that it implements a method of simulating streamer positioning according to any of the above-mentioned features.
Preferred but non-limiting features of the method of the invention for assisting navigation are as follows:
it comprises determining the set of {ship position; instant} pairs at regular intervals in space so as to define a track along which the orientation of the streamer at a given abscissa along the general orientation of the lines of the array is as close as possible to the orientation of an associated streamer during a previous pass of the ship along an adjacent line;
the method comprises the following steps:
selecting a xe2x80x98current objectxe2x80x99 of appropriate type;
defining optimization parameters;
computing the positioning of a xe2x80x98reference streamerxe2x80x99 from data relating to the streamer positioning of the adjacent profile and the optimization parameters;
taking account of ship speed and direction data and streamer positioning data at the time optimization computation is started;
creating a three-dimensional optimization grid with a first dimension (Y) parallel to said general direction, a second direction (X) being perpendicular to the general direction, and included in the horizontal plane, and the third dimension (DT) representing possible time increments between two nodes spaced apart by one grid cell in the general direction (Y);
simulating variations in the positioning of the streamer towed by a ship following all of the tracks defined by the nodes of the optimization grid;
for all of the possible tracks, computing a norm of the difference between simulated streamer positioning and reference streamer positioning; and
computing an optimum track for which the associated norm is a minimum;
the optimization step comprises minimizing a norm of the difference between reference streamer positioning and simulated streamer positioning;
said normal to be minimized has the form:       H    ⁡          (              X1        ,                  δ          ⁢                      xe2x80x83                    ⁢          t1                    )        =                    ∑                  j          =          1                J            ⁢              ∑                  k          =          1                K              ❘                                        X            reference                    ⁡                      (                          k              ,              j                        )                          -                              X            predicted                    ⁡                      (                          k              ,              j                        )                              ❘              f        ⁡                  (          k          )                    
xe2x80x83where:
X1 is a series of J consecutive values for the position of the streamer head along the horizontal direction of the optimization grid perpendicular to the general direction;
xcex4t1 is a series of J consecutive values for the duration taken by the streamer head to pass form one node of the optimization grid of coordinates (Xi1, Yj, xcex4tk1) to a node having coordinates (Xi2, Yj+1, xcex4tk2),
J is the number of nodes of the grid in said general direction (Y);
K is the number of curvilinear abscissa points along the discretized streamer;
Xreference(k,j) is the position along the X axis of the point xe2x80x9ckxe2x80x9d of the xe2x80x98reference streamerxe2x80x99 when the head thereof is at the jth plane of the optimization grid along the Y axis;
Xpredicted(k,j) is the position along the X axis of the point xe2x80x9ckxe2x80x9d of the simulated streamer when the head thereof is at the jth plane of the optimization grid along the Y axis; and
f(k) is a weighting function applied to the difference between the simulated streamer and the reference streamer;
the method implements an optimization criterion for said difference between the measured and predicted streamer-positioning data; and
the step of optimizing zone coverage is implemented in real time so as to provide the ship with a series of {instant; ship position; ship speed} triplets to follow so as to optimize the path of the ship along a line that the ship is surveying.
The invention also proposes an application of the method of assisting navigation as outlined above, to determining a path and a starting time associated with a forthcoming line that is to be surveyed by the ship, and also for determining the best forthcoming line to survey. In this application, in a preferred feature, a line starting time is sought from within a given time window that corresponds to minimizing undercoverage and overcoverage.
Finally, the invention provides a method of predicting the coverage fraction associated with an operation of acquiring geophysical data that is to be performed at sea over a given zone, the method being characterized in that it implements simulating the track of a ship including a method of assisting navigation as outlined above.